Question: Gabriela is 40 years older than Kevin. Five years ago, Gabriela was 5 times as old as Kevin. How old is Kevin now?
Explanation: We can use the given information to write down two equations that describe the ages of Gabriela and Kevin. Let Gabriela's current age be $g$ and Kevin's current age be $k$ The information in the first sentence can be expressed in the following equation: $g = k + 40$ Five years ago, Gabriela was $g - 5$ years old, and Kevin was $k - 5$ years old. The information in the second sentence can be expressed in the following equation: $g - 5 = 5(k - 5)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$ , it might be easiest to use our first equation for $g$ and substitute it into our second equation. Our first equation is: $g = k + 40$ . Substituting this into our second equation, we get the equation: $(k + 40)$ $-$ $5 = 5(k - 5)$ which combines the information about $k$ from both of our original equations. Simplifying both sides of this equation, we get: $k + 35 = 5 k - 25$ Solving for $k$ , we get: $4 k = 60$ $k = 15$.